The inspiration for using a superposition principle stems from similar approaches in [1]}, [2]}, where it is applied to transport equations lifted from the Boltzmann-equation or mean-field jump dynamics respectively, and the main ingredient is the abstract superposition principle over \(\mathbb {R}^\mathbb {N}\)  of [3]}. However, these results are not directly applicable to our setting, since the mass of \(\nu _t(\mathcal {T})\)  for a mean-field curve is not fixed, and \(V[\nu ](\mathcal {T})\)  is finite but unbounded over \(\Gamma \) . We remedy this by combining two known superposition principles: on the one hand, the abstract superposition principle over \(\mathbb {R}^\mathbb {N}\)  of [3]}, and on the other hand one for finite-dimensional vector fields with linear growth, found in [5]}. Our result is stated in Theorem REF .
